Right orderable groups that are not locally indicable. (English) Zbl 0677.06007

The universal covering group of SL(2,\({\mathbb{R}})\) is right orderable, but it is shown that it is not locally indicable, and in fact has finitely generated perfect subgroups. (The question was open among ordered-group theorists whether every right orderable group was locally indicable, i.e., had the property that all nontrivial finite generated subgroups admitted homomorphisms to the infinite cyclic group. After preparing this paper, the author was informed of a similar, unpublished, example known to some tpologists; this is also sketched.) Some still-open cases are noted.
Reviewer: G.M.Bergman


06F15 Ordered groups
20E25 Local properties of groups
57M10 Covering spaces and low-dimensional topology
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